The phrase "arithmetical problems and" is correct and usable in written English.
It can be used when discussing topics related to mathematics, specifically in the context of problems or exercises involving arithmetic.
Example: "In our math class, we will focus on arithmetical problems and their practical applications in everyday life."
Alternatives: "mathematical problems and" or "numerical problems and".
Of course solving arithmetical problems in arithmetic is in some cases practically impossible.
Shapes and sculptures, arithmetical problems, linguistic points moved easily around each other.
Detlefsen has emphasized that the incompleteness theorems do not preclude that the consistency of parts of higher mathematics that are in practice used for solving arithmetical problems that mathematicians are interested in can be arithmetically established (Detlefsen 1986).
Some indices incorporate arithmetical problems.
After the training, a "mental abacus" was formed in their brains [ 15, 20], which may be helpful when they performed the arithmetical problems.
When solving arithmetical problems, participants with high maths anxiety have higher error rates, they have problems with rejecting incorrect solutions (even when these are highly implausible), and these effects are especially prominent in the case of more complex problems which require a carry operation (e.g., [ 15, 16]).
The problem was twice part of a short story (STORY; e.g., Anna goes for a walk. She walks 4 kilometers per hour. What distance does she cover in 3 hours?), and once the arithmetical problem was formulated (FORMULATION; e.g., What result do you obtain when multiplying 3 by a factor of 4?).
The following example is a typical arithmetical problem that is expressed by the triplet structure model in a combination story: {There are 3 white rabbits (first existence sentence).
The following is a typical arithmetical problem that is expressed by the triplet structure model in a decrease story: {There are 5 apples (first existence sentence).
If the only ways of proving the consistency of arithmetic make essential use of notions which arguably belong to higher-order mathematics, then the consistency of arithmetic, even though it can be expressed in the language of Peano Arithmetic, is a non-arithmetical problem.
